Bell's theorem without inequalities for one class of two-qubit mixed states

Łukasz Derkacz, Lech Jakóbczyk

Joanna K. Kalaga, W. Leoński, Jan Peřina

We discuss a family of W-class states describing three-qubit systems. For such systems, we analyze the relations between the entanglement measures and the nonlocality parameter for a two-mode mixed state related to the two-qubit subsystem. We find the conditions determining the boundary values of the negativity, parameterized by concurrence, for violating the Bell-CHSH inequality. Additionally, we derive the value ranges of the mixedness measure, parameterized by concurrence and negativity for the qubit-qubit mixed state, guaranteeing the violation and non-violation of the Bell-CHSH inequality.

Marek Żukowski, Časlav Brukner

We derive a single general Bell inequality which is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodecki family condition for two qubits.

Arpan Das, Chandan Datta, Pankaj Agrawal

Su-Kuan Chu, Chen-Te Ma, Rong-Xin Miao +1 more

Marek Żukowski, Časlav Brukner

Abstract We present a single general Bell inequality that summarizes all possible Bell type constrains on the correlation function for the N‐particle system (i.e., it is a necessary and sufficient condition for the existence of local realistic models for the correlation function). It is applicable in the case when measurements on each particle can be chosen between two arbitrary dichotomic observables. We also obtain a necessary and sufficient condition for an arbitrary N‐qubit mixed state to violate this general Bell inequality.